The present invention relates to a method of analyzing the structure of a medium. While the invention has a number of possible applications, including tomography or non-destructive testing of a body, it is particularly useful in seismic prospecting for determining the physical structure of the earth at any particular location, and is therefore described below with respect to this application.
It is generally accepted that the Common Middle Point (CMP) method, also sometimes called the Common Depth Point (CPD) method, of seismic prospecting has changed the philosophy, style and technique of reflection surveying in seismic prospecting and has caused drastic qualitative and quantitative improvements in seismic data interpretation. The crucial point of the CMP technique is a stack. However, it is well-known that a stack of observed data is usually accompanied by a loss of information (resolution) as compared to unstacked data. This is true for the CMP stack in all situations involving non-horizontally layered media and/or a dipping reflector.
Different methods (e.g., deep moveout and all its modifications) were proposed to eliminate, or at least to diminish, this undesirable property of stacking. However, the known methods generally have the drawback that it is necessary to know beforehand the velocity structure of the overburden and reflector dip. Determinining the velocity structure with the required accuracy is extremely difficult in practice especially in case of complicated media.
It would therefore be very desirable to develop a method of data stacking which: (1) does not demand any prior knowledge of the parameters of the overburden structure, (2) results in collecting and enhancing useful waves, and (3) does not involve a loss of information concerning target objects.
A method meeting all the above three characteristics was proposed by the inventor in Israel Patent Application 83306 filed July 23, 1987, which corresponds to U.S. patent application Ser. No. 07/217,269 filed July 11, 1988, which issued as U.S. Pat. No. 4,878,205 on Oct. 31, 1989. The described method, called the CRE (Common Reflecting Element) method is distinguished from traditional data processing techniques primarily by the following two main characteristics: (1) the stacking of the studied traces of one gather should correpond to a special type of an asymmetrical non-uniform distribution (called a polynomial or binomial distribution) of corresponding source-receiver pairs; and (2) the stacked traces should be subjected to a particular type of time correction, called the Oblique Circle Correction (OSC), which depends only on local parameters of wavefronts with respect to the receivers and sources placed along a seismic line.
The CRE method does not use the velocity characteristics of the overburden, like the velocity in the well-known formula .DELTA.t=.sqroot.t.sub.o.sup.2 +.DELTA.X.sup.2 /V.sup.2-2, or average velocity, or internal velocity. Both the polynomial distribution and the OSC (Oblique Spherical Correction) are applicable for two-dimensional overburdens of an arbitrary structure. Usually in practice the parameters of the distribution and the OSC are unknown. Therefore, a special procedure for a search of optimal values of such parameters is proposed using traces recorded in the field according to an arbitrary multi-fold system of observation.
It would appear at first glance that only the CRM method satisfies all three of the desirable characteristics set forth above. Actually, only one type of a source-receiver configuration, namely the polynomial distribution, corresponds to the CRP method, although approximatations could be obtained by some mathematical transformation of the polynomial distribution.
However, if this problem is more carefully studied, it becomes clear that many methods could satisfy all three of the above characteristic conditions, because of the following observations: In the CRE method, each point of a reflector (i.e., each of the CRP's) is uniquely mapped in one point of the corresponding image surface, and vice versa. This means that, from the mathematical point of view, a reflector and its CRE image are topologically equivalent. This property of the CRE mapping preserves the information concerning a mapped reflector by the CRE stack. In mathematics, it is well-known that a typologically equivalent mapping is not unique. Thus, generally speaking, there would be many types of typologically equivalent stacks.